Thermodynamic and dynamical properties of filling-control metal-insulator transition (MIT) in the Hubbard model are studied by the operator projection method, especially in two dimensions. This is a non-perturbative analytic approach to many-body systems. The present theory incorporates the Mott-Hubbard, Brinkman-Rice and Slater pictures of the MIT into a unified framework, together with reproducing low-energy narrow band arising from spin-charge fluctuations. At half filling, single-particle spectra $A(ω, k)$ show formation of two Hubbard bands and their antiferromagnetic shadows separated by a Mott gap in the plane of energy $ω$ and momentum $k$ with lowering temperatures. These four bands produce splitting to two low-energy narrow bands and two SDW-like bands in the dispersion. Near half filling, the low-energy narrow band persists at low temperatures. This narrow band has a particularly weak dispersion and large weights around $(π, 0)$ and $(0, π)$ momenta. The velocity of these low-energy excitations is shown to vanish towards the MIT, indicating the mass divergence as in the Brinkman-Rice picture, but most prominently around $(π,0)$ and $(0,π)$ with strong momentum dependence. This reflects the suppression of the coherence near the MIT. Main structures in $A(ω, k)$ show remarkable similarities to quantum Monte-Carlo results in two dimensions as well as in the one-dimensional Hubbard model. The charge compressibility appears to diverge with decreasing doping concentration in both one and two dimensions in agreement with the exact and quantum Monte-Carlo results. We also discuss implications of the flat dispersion formed near the Fermi level to the observations in high-$\Tc$ cuprate superconductors.Thermodynamic and dynamical properties of filling-control metal-insulator transition (MIT) in the Hubbard model are studied by the operator projection method, especially in two dimensions. This is a non-perturbative analytic approach to many-body systems. The present theory incorporates the Mott-Hubbard, Brinkman-Rice and Slater pictures of the MIT into a unified framework, together with reproducing low-energy narrow band arising from spin-charge fluctuations. At half filling, single-particle spectra $A(ω, k)$ show formation of two Hubbard bands and their antiferromagnetic shadows separated by a Mott gap in the plane of energy $ω$ and momentum $k$ with lowering temperatures. These four bands produce splitting to two low-energy narrow bands and two SDW-like bands in the dispersion. Near half filling, the low-energy narrow band persists at low temperatures. This narrow band has a particularly weak dispersion and large weights around $(π, 0)$ and $(0, π)$ momenta. The velocity of these low-energy excitations is shown to vanish towards the MIT, indicating the mass divergence as in the Brinkman-Rice picture, but most prominently around $(π,0)$ and $(0,π)$ with strong momentum dependence. This reflects the suppression of the coherence near the MIT. Main structures in $A(ω, k)$ show remarkable similarities to quantum Monte-Carlo results in two dimensions as well as in the one-dimensional Hubbard model. The charge compressibility appears to diverge with decreasing doping concentration in both one and two dimensions in agreement with the exact and quantum Monte-Carlo results. We also discuss implications of the flat dispersion formed near the Fermi level to the observations in high-$\Tc$ cuprate superconductors.

arXiv:cond-mat/0107291Journal of the Physical Society of JapanNov 1, 200133 citations

Superconductivity in the two-band Hubbard model

Masahisa Koga, Akihisa Koga

Jan 1, 20150 citations

Polaron conductivity in the narrow-band Hubbard model

Yuhei Suzuki, Philip A. Pincus, Alan J. Heeger

We consider a Hubbard model in which electrons are locally coupled to the lattice and form polarons. The frequency-dependent polaron conductivity ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{pot}}$(\ensuremath{\omega}) is calculated in the narrow-band limit as a function of electron density. There are two contributions: a band term that arises from coherent motion of dressed electrons and a hopping term that describes the incoherent process by which electrons ``shake off'' their polaron distortion. The possible relevance of these results to the structure in \ensuremath{\sigma}(\ensuremath{\omega}) observed in high- ${\mathit{T}}_{\mathit{c}}$ superconductors is briefly discussed.We consider a Hubbard model in which electrons are locally coupled to the lattice and form polarons. The frequency-dependent polaron conductivity ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{pot}}$(\ensuremath{\omega}) is calculated in the narrow-band limit as a function of electron density. There are two contributions: a band term that arises from coherent motion of dressed electrons and a hopping term that describes the incoherent process by which electrons ``shake off'' their polaron distortion. The possible relevance of these results to the structure in \ensuremath{\sigma}(\ensuremath{\omega}) observed in high-${\mathit{T}}_{\mathit{c}}$ superconductors is briefly discussed.

Physical review. B, Condensed matterOct 1, 199111 citations

On superconductivity in the two-band Hubbard model

V. A. Moskalenko, S. P. Kozhokaru, Nguyen Thi Que

Soviet Journal of Low Temperature PhysicsOct 1, 19910 citations

Polaron in Tight Binding Models with Coulomb Correlation

Ashok Chatterjee, Soma Mukhopadhyay

This chapter introduces the Hubbard model and the Holstein-Hubbard model and discusses the charge-density wave-spin density wave transition. The most suitable model to study the interplay between the electron-phonon interaction and the Coulomb repulsion in narrow-band systems is the Holstein-Hubbard model. Krishna, Mukhopadhyay, and Chatterjee have considered an extended Holstein-Hubbard model in one dimension so that the exact Bethe ansatz solution can be taken advantage of for the effective electronic problem and employed a better phonon variational state. The chapter also discusses the nature of the self-trapping (ST) transition, particularly whether the transition is continuous or discontinuous. In view of the potential role of small polarons in high Tc superconductors and colossal magneto-resistance materials, it is certainly more important to understand the nature of the ST transition in small polaron models. Das and Sil have studied the ST transition for a many-polaron system in the two-dimensional HH model.This chapter introduces the Hubbard model and the Holstein-Hubbard model and discusses the charge-density wave-spin density wave transition. The most suitable model to study the interplay between the electron-phonon interaction and the Coulomb repulsion in narrow-band systems is the Holstein-Hubbard model. Krishna, Mukhopadhyay, and Chatterjee have considered an extended Holstein-Hubbard model in one dimension so that the exact Bethe ansatz solution can be taken advantage of for the effective electronic problem and employed a better phonon variational state. The chapter also discusses the nature of the self-trapping (ST) transition, particularly whether the transition is continuous or discontinuous. In view of the potential role of small polarons in high Tc superconductors and colossal magneto-resistance materials, it is certainly more important to understand the nature of the ST transition in small polaron models. Das and Sil have studied the ST transition for a many-polaron system in the two-dimensional HH model.

CRC Press eBooksOct 9, 20180 citations

A(ω, k)

show formation of two Hubbard bands and their antiferromagnetic shadows separated by a Mott gap in the plane of energy

ω

and momentum

k

with lowering temperatures. These four bands produce splitting to two low-energy narrow bands and two SDW-like bands in the dispersion. Near half filling, the low-energy narrow band persists at low temperatures. This narrow band has a particularly weak dispersion and large weights around

(π, 0)

and

(0, π)

momenta. The velocity of these low-energy excitations is shown to vanish towards the MIT, indicating the mass divergence as in the Brinkman-Rice picture, but most prominently around

(π,0)

and

(0,π)

with strong momentum dependence. This reflects the suppression of the coherence near the MIT. Main structures in

A(ω, k)

show remarkable similarities to quantum Monte-Carlo results in two dimensions as well as in the one-dimensional Hubbard model. The charge compressibility appears to diverge with decreasing doping concentration in both one and two dimensions in agreement with the exact and quantum Monte-Carlo results. We also discuss implications of the flat dispersion formed near the Fermi level to the observations in high-$\Tc$ cuprate superconductors.

{\mathit{T}}_{\mathit{c}}

superconductors is briefly discussed.